
In this work, we derive closed-form expressions for the parameters controlling the stability of the synchronisation manifold of identical maps, diffusively coupled in regular graphs – graphs were all the nodes have the same degree – and cyclic graphs – regular graphs with cyclical permutation symmetries. Our detailed derivations are based on the Master Stability Function (MSF) [1]}, [2]} and the spectral properties of the graph's Laplacian matrix [3]}, [4]}, [5]} (giving expressions for its eigenvalues), complementing the broad literature of synchronisation in coupled map lattices [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]} with specific parameter expressions that can be applied straightforwardly.
